Interpretation of seismic data, for example, in determining locations of candidate petroleum reservoirs, is typically based on various techniques of visualizing processed seismic sections. Traditionally, two-dimensional (2-D) seismic interpretation is based on a migrated post-stack seismic section—often referred to simply as the seismic section—for visualization. The migrated post-stack seismic section shows amplitudes of fully processed seismic traces as functions of time and Common Depth Point (CDP) position.
With the emergence of three-dimensional (3-D) seismic techniques, the 2-D seismic sections have been largely replaced by 2-D “slices”—horizontal or vertical—through 3-D seismic data. However, like traditional 2-D data, these are likely contaminated by noise during data capture, and are distorted during subsequent data processing, for example, due to “edge effects” introduced by the migration processing step.
While an experienced interpreter of seismic data is able to disregard noise and artifacts, inevitably there arise instances in which subtle features that the interpreter needs to see are obscured. As a consequence, the interpreter is not able to provide sufficient information, for example, about the location of a candidate petroleum reservoir, requiring more seismic investigations, or worse, the interpretation is incorrect. Both scenarios result in substantial additional costs.
It is known in the art that local spectral content—texture—of multi-dimensional signals differs from textures of noise and artifacts. The most commonly used method of spectral representation of an image is the Fourier transform, which describes the content of a signal entirely in frequency domain. Although the Fourier transform is a powerful tool, its lack of positional resolution renders it ill-suited for describing local, or pixel-to-pixel, changes in spectral content of multi-dimensional data.
It would be highly desirable to provide an improved method for processing multi-dimensional signal data to determine frequency dependent features therefrom based on a transform capable of resolving local, or pixel-to-pixel, changes in space or time-space and frequency. It would be further highly beneficial to provide better visualization of the frequency dependent features.